Well, this gets complicated and legal. (Caveat: I am not a lawyer.) According to Creative Commons, their licenses:
give everyone from individual creators to large companies and institutions a simple, standardized way to grant copyright permissions to their creative work.
In short, CC licenses apply to creative works and are meant to relax or waive the copyright protections automatically guaranteed to authors (e.g., by common law tradition in Commonwealth countries).
The applicability of CC licenses to data depends on whether data can be copyrighted. If data cannot be copyrighted, then there is no point to putting a CC license on them because those licenses waive rights that the data creators do not have.
So what kinds of works are protected by copyright? Though laws vary across jurisdictions (and thus make this question difficult to answer), two important principles are the "Idea-Expression divide" and "the threshold of originality". In the former, only expressions of ideas can be copyrighted, while ideas themselves cannot be. In the latter, among expressions, only those that are original are protected (thus reproductions of works do not earn copyright protection de novo).
Thus data only have copyright protection if they are an expression of an idea rather than idea itself and if they are not simply "facts" (i.e., they are something sufficiently original).
- In the United States, this almost universally means that data cannot be copyrighted. A classic legal case here is Feist Publications, Inc., v. Rural Telephone Service Co., which ruled that telephone number listings in a phonebook are not protected by copyright. Importantly, nothing produced by the federal government has copyright protection (all federal government works are in the public domain, but this does not necessarily apply to other levels of government).
- In Europe, however, databases do have copyright-like protection. Not all databases are protected; protection comes from "qualitatively and/or quantitatively a substantial investment in either the obtaining, verification or presentation of the contents". Such rights extend for 15 years.
Thus, one has to determine whether the "data" being discussed merit copyright on their own. It may be that "data" refer to works that are themselves copyrighted (e.g., original written works, such as newspaper articles). Those "data" are protected but not because they are data, rather because they are creative works. Someone who has compiled those works into a database in the United States has no copyright protection for the works (unless they have obtained those rights for each "data point" from the original author(s)). In Europe, however, the compilation of those data into a database may entitle the compiler to a limited database right.
In conclusion, CC licenses make sense if one has copyright protections to give away. If not, then CC licenses make no sense because the data are probably free to use anyway. If the data do merit protection (due to either satisfying European-style threshold of investment, or American-style threshold of originality, or some other national standard), then I believe the argument made in the linked webpage is purely made on the opinion that CC0/(or Public Domain, where that principle exists) are preferable to more restricted waivers of rights.
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